Say I want to transfer several dump files from a Solaris machine onto a Win2k machine for storage. It was suggested that I tar and gzip the dump files before doing so.

Is it completely necessary to use both of these utilities, or is it sufficient to compress multiple dump files into one gzip file? Also, if tar is necessary, what does it do exactly for the files in question?

tar will group all the files in question into one ".tar" file. gzip will do the actual compression.

why not do a man on tar and gzip for more info.

You may also want to use the "mv" utility to rename the compressed archive from ".tar.gz" to ".tgz" so that Winzip can open it.

P.S. I believe GNU tar has a "compress" option.

I have been poring over the man pages. I think I understand now.

I was under the impression that I could gzip file1 file2 file3 file4 and it would produce a single gzipped file. I guess you have to tar them into one file first. Is this accurate?

In solaris gzip only compresses the files. It will not produced a single gzipped file when presented with multiple files as arguments, it will merely gzip them up individually:
So you are correct. you need to tar the files first.